Go to Control Panel > Flash Player > Storage
Choose Allow sites to save information on this computer
This will suppress this dialog, and will allow websites to store information for their applications.
You can delete this information through the Control Panel > Flash Player > Advanced > Delete All, or just by clearing the cookies in your browser. When you're using Private Browsing or Incognito mode, the infromation is stored, but in a temporary directory that gets deleted when you exit private browsing mode. This approach is way better than disabling the various storage features of Flash as the content doesn't know that it's in private browsing mode, and won't degrade the experience by throwing permission dialogs when things are explicitly disallowed.